The symmetries of McCullough-Miller space

Abstract

We prove that if \(W\) is the free product of at least four groups of order 2, then the automorphism group of the McCullough-Miller space corresponding to \(W\) is isomorphic to group of outer automorphisms of \(W\). We also prove that, for each integer \(n \geq 3\), the automorphism group of the hypertree complex of rank \(n\) is isomorphic to the symmetric group of rank \(n\).